Nonparametric Kernel Density Estimation Research Articles

Track-before-Detect Algorithm for Underwater Diver Based on Knowledge-Aided Particle Filter.

This work studies the underwater detection and tracking of diver targets under a low signal-to-reverberation ratio (SRR) in active sonar systems. In particular, a particle filter track-before-detect based on a knowledge-aided (KA-PF-TBD) algorithm is proposed. Specifically, the original echo data is directly used as the input of the algorithm, which avoids the information loss caused by threshold detection. Considering the prior motion knowledge of the underwater diver target, we established a multi-directional motion model as the state transition model. An efficient method for calculating the statistical characteristics of echo data about the extended target is proposed based on the non-parametric kernel density estimation theory. The multi-directional movement model set and the statistical characteristics of the echo data are used as the knowledge-aided information of the particle filter process: this is used to calculate the particle weight with the sub-area instead of the whole area, and then the particles with the highest weight are used to estimate the target state. Finally, the effectiveness of the proposed algorithm is proved by simulation and sea-level experimental data analysis through joint evaluation of detection and tracking performance.

Trivariate Joint Distribution Modelling of Compound Events Using the Nonparametric D-Vine Copula Developed Based on a Bernstein and Beta Kernel Copula Density Framework

Low-lying coastal communities are often threatened by compound flooding (CF), which can be determined through the joint occurrence of storm surges, rainfall and river discharge, either successively or in close succession. The trivariate distribution can demonstrate the risk of the compound phenomenon more realistically, rather than considering each contributing factor independently or in pairwise dependency relations. Recently, the vine copula has been recognized as a highly flexible approach to constructing a higher-dimensional joint density framework. In these, the parametric class copula with parametric univariate marginals is often involved. Its incorporation can lead to a lack of flexibility due to parametric functions that have prior distribution assumptions about their univariate marginal and/or copula joint density. This study introduces the vine copula approach in a nonparametric setting by introducing Bernstein and Beta kernel copula density in establishing trivariate flood dependence. The proposed model was applied to 46 years of flood characteristics collected on the west coast of Canada. The univariate flood marginal distribution was modelled using nonparametric kernel density estimation (KDE). The 2D Bernstein estimator and beta kernel copula estimator were tested independently in capturing pairwise dependencies to establish D-vine structure in a stage-wise nesting approach in three alternative ways, each by permutating the location of the conditioning variable. The best-fitted vine structure was selected using goodness-of-fit (GOF) test statistics. The performance of the nonparametric vine approach was also compared with those of vines constructed with a parametric and semiparametric fitting procedure. Investigation revealed that the D-vine copula constructed using a Bernstein copula with normal KDE marginals performed well nonparametrically in capturing the dependence of the compound events. Finally, the derived nonparametric model was used in the estimation of trivariate joint return periods, and further employed in estimating failure probability statistics.

Water Quality Criteria and Ecological Risk Assessment of Typical Transition Metals in South Asia.

Transition metal pollution in rivers in South Asia is more serious than in other regions because of the lack of adequate freshwater management measures. Water quality criteria (WQC) for South Asia is urgently needed to protect regional aquatic environments because of the occurrence of transboundary rivers. The present study established non-parametric kernel density estimation species sensitivity distribution (NPKDE-SSD) models and then derived the acceptable hazardous concentration for protection of 95% of all aquatic species (HC5) and WQC of six typical transition metals in South Asia. The results showed that the order of acute and chronic WQC was Mn > Fe > Cd > Zn > Cu > Hg and Cu > Fe > Cd, respectively. A risk assessment of these metals in the Indus River, the Ganges River, the Brahmaputra River, the Meghna River, and the Bagmati River was also carried out. Based on the results, these major rivers in South Asia were highly polluted with transition metals, with significant ecological risks for a large number of aquatic species. This study can contribute to a better understanding of ecological risks in South Asia and provide a scientific basis for the updating of water quality standards and the increase in overall water quality.

Working Condition Recognition of a Mineral Flotation Process Using the DSFF-DenseNet-DT

The commonly used working condition recognition method in the mineral flotation process is based on shallow features of flotation froth images. However, the shallow features of flotation froth images frequently have an excessive amount of redundant and noisy information, which has an impact on the recognition effect and prevents the flotation process from being effectively optimized. Therefore, a working condition recognition method for the mineral flotation process based on a deep and shallow feature fusion densely connected network decision tree (DSFF-DenseNet-DT) is proposed in this paper. Firstly, the color texture distribution (CTD) and size distribution (SD) of a flotation froth image obtained in advance are approximated by the nonparametric kernel density estimation method, and a set of kernel function weights is obtained to represent the color texture and size features, while the deep features of the flotation froth image are extracted through the densely connected network (DenseNet). Secondly, a two-stage feature fusion method based on a stacked autoencoder after Concat (Cat-SAE) is proposed to fuse and reduce the dimensionality of the extracted shallow features and deep features so as to maximize the comprehensive description of the features and eliminate redundant and noisy information. Finally, the feature vectors after fusion dimensionality reduction are fed into the densely connected network decision tree (DenseNet-DT) for working condition recognition. Multiple experiments employing self-built industrial datasets reveal that the suggested method’s average recognition accuracy, precision, recall and F1 score reach 92.67%, 93.9%, 94.2% and 0.94, respectively. These results demonstrate the proposed method’s usefulness.

Flood forecasting and uncertainty analysis based on the combination of improved adaptive noise learning model and density estimation

AbstractThe strong randomness exhibited by runoff series means the accuracy of flood forecasting still needs to be improved. Mode mixing can be dealt with using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), and the endpoint effect of CEEMDAN can be successfully dealt with using the mutual information criterion. To increase the computational effectiveness of broad learning (BL), orthogonal triangular matrix decomposition (QR) was used. A novel improved coupled CEEMDAN-QRBL flood forecasting model was created and applied to the prediction of daily runoff in Xiaolangdi Reservoir based on the benefit of quick calculation by the model output layer. The findings indicate that the enhanced QRBL is 28.92% more computationally efficient than the BL model, and that the reconstruction error of CEEMDAN has been decreased by 48.22%. The MAE of the improved CEEMDAN-QRBL model is reduced by 12.36% and 16.31%, and the Ens is improved by 8.81% and 3.96%, respectively, when compared with the EMD-LSTM and CEEMDAN-GRU models. The predicted values of the CEEMDAN-QRBL model have a suitable fluctuation range thanks to the use of nonparametric kernel density estimation (NPKDE), which might serve as a useful benchmark for the distribution of regional water resources.

Multi-sensor optimal placement of rotor-bearing system based on fault diagnosability

In view of the current situation that there are few studies on whether the fault signals that may occur in the rotor bearing system can be identified and analyzed in the sensor arrangement, fault diagnosability is applied to the optimal arrangement of the sensors in the rotor bearing system. The preliminary layout of the multi-sensor is carried out by analyzing the transmission path of the vibration signals in the rotor bearing system and based on the minimum path. Secondly, the nonparametric kernel density estimation method calculates the state information’s probability density function. The K-L divergence value is further used to measure fault detectability, fault separability, and fault diagnosability. Then, the correlation function method is used to fuse the multi-sensor information, and the optimal sensor layout is given with the fault diagnosability as an index. Finally, the validity of the method is proved by the experimental laboratory data and the correlation coefficient.

AUTOMATIC BUILDING FOOTPRINT EXTRACTION FROM 3D LASERSCANS

Abstract. Building footprints are a prerequisite for many tasks such as urban mapping and planning. Such structures are mostly derived using airborne laser scanning which reveals rather roof structures than the underlying hidden footprint boundary. This paper introduces an approach to extract a 2D building boundary from a 3D point cloud stemming from either terrestrial scanning or via close-range sensing using a mobile platform, e.g. drone. To this end, a pipeline of methods including non-parametric kernel density estimation (KDE) of an underlying probability density function, a solution of the Travelling Salesperson Problem (TSP), outlier elimination and line segmentation are presented to extract the underlying building footprint. KDE turns out to be suitable to automatically determine a horizontal cut in the point cloud. An ordering of the resulting points in this cut using a shortest possible tour based on TSP allows for the application of existing line segmentation algorithms, otherwise dedicated to indoor segmentation. Outliers in the resulting segments are removed using Density-Based Spatial Clustering of Applications with Noise (DBSCAN). The segments are then generalized leading to the final footprint geometry. We applied our approach on real-world examples and achieved an IoU between 0.930 and 0.998 assessed by ground truth footprints from both authoritative and volunteered geographic information (VGI) data.

Nonparametric Approach to Copula Estimation in Compounding The Joint Impact of Storm Surge and Rainfall Events in Coastal Flood Analysis

The joint probability modelling of storm surges and rainfall events is the main task in assessing compound flood risk in low-lying coastal areas. These extreme or non-extreme events may not be dangerous if considered individually but can intensify flooding impact if they occur simultaneously or successively. Recently, the copula approach has been widely accepted in compound flooding but is often limited to parametric or semiparametric distribution settings in a limited number of cases. However, both parametric and semiparametric approaches assume the prior distribution type for univariate marginals and copula joint density. In that case, there is a high risk of misspecification if the underlying assumption is violated. In addition, both approaches suffer from a lack of flexibility. This study uses bivariate copula density in the nonparametric distribution setting. The joint copula structure is approximated nonparametrically by employing the Bernstein copula estimator and Beta kernel copula density, and their performances are also compared. The proposed model is tested with 46 years of rainfall and storm surge observations collected on Canada's west coast. The marginal distribution of the selected flood variables is modelled using nonparametric kernel density estimation (KDE). Based on the different model compatibility tests, the Bernstein copula with normal KDE margins defined the joint dependence structure well. The selected nonparametric copula model is further employed to estimate joint and conditional return periods. It is found that flood hazard characteristics occurrence simultaneously is less frequent in AND-joint cases than in OR-joint cases. Also, the derived model is further used to estimate failure probability (FP) statistics to assess the variation of bivariate hydrologic risk during the project lifetime. It is found that FP statistics could be underestimated when neglecting the compound effect of storm surge and rainfall in the coastal flood risk.

Assessment of various seismic fragility analysis approaches for structures excited by non-stationary stochastic ground motions

A probabilistic assessment is performed using different seismic fragility analysis approaches for structures under non-stationary stochastic ground motions. Four commonly used probabilistic seismic fragility analysis (PSFA) approaches are adopted, which are least squares regression (LSR), maximum likelihood estimation (MLE), kernel density estimation (KDE) and Monte Carlo simulation (MCS). The principles of the four PSFA approaches are first introduced, and the theories of non-stationary stochastic acceleration time series are introduced in light of the spectral representation of random functions. Then an analytical procedure of different PSFA approaches is constructed for structures under non-stationary stochastic motions. After that a case study is carried out to analyze the results of the four PSFA approaches. The demand distributions of univariate random variable under certain intensity measure levels are discussed, and multiple fragility curves under different limit states for all the approaches are compared. In general, the MCS approach is set as the benchmark to verify the effectiveness of other approaches, but it is computationally consuming. The non-parametric KDE approach is recommended to estimate the univariate distribution under specified IM levels, because it can reflect the real distribution characteristics with combined efficiency and accuracy. For the seismic fragility under different limit states, the LSR approach is suitable for efficient data processing and general trend assessment, at the expense of accuracy. The MLE approach indicates a better applicability under a smaller response threshold and slighter damage conditions, while the KDE approach shows a better applicability under a larger response threshold and severer damage conditions. The paper compares the accuracy and applicability of various PSFA approaches under multiple conditions, and provides a basis to link probabilistic hazard and risk analyses for performance assessment in the future research.

An integrated approach for identification and quantification of ecological drought in rivers from an ecological streamflow perspective

Although various studies have investigated the impacts of climate variability and human activities on drought, researches specifically analysing the impact on ecological drought are still limited. A deep understanding of the climatic and anthropogenic effects on ecological drought processes is crucial for ecological regulation and management in the changing environments. In the present study, an integrated approach for comprehensive understanding and quantification of ecological drought in rivers was proposed which first applied the nonparametric kernel density estimation (KDE) method to calculate the most suitable ecological streamflow (MSES) for a river ecosystem. Then, the variable threshold level method based on the MSES for each month and the run theory method were applied to identify the ecological drought duration and deficit volumes. Finally, a quantification approach based on hydrological model simulation was proposed to attribute the impacts of climate variability and human activities on ecological drought. The proposed approach was applied on two catchments, Xianyang (XY) and Huaxian (HX) within the Weihe River Basin (WRB) in northern China. Comparison results obtained using the two empirical methods revealed that the MSES calculated using the KDE method was reasonable and can be used for ecological drought identification. The identification results showed that both the median and upper quartile values of the drought duration and deficit volumes during the disturbed period (1991–2017) were greater than those during the undisturbed period (1961–1990). Quantification results showed that human activities were the dominant factor aggravating ecological drought in the WRB after 1990. The contribution rates of climate variability and human activities toward ecological drought variations were 25.6% and 74.4%, respectively, for the XY station and 42.7% and 57.3%, respectively, for the HX station. Although the WRB was selected as a case study, the proposed approach can also be applied to other regions to provide scientific guidance for regional ecological management.

Robust Under-Frequency Load Shedding With Electric Vehicles Under Wind Power and Commute Uncertainties

Under-frequency load shedding (UFLS) is an important measure for tackling low-frequency events caused by load-generation imbalance. However, the uncertainty of wind power amplifies power imbalances and can potentially impair frequency stability. Electric vehicles (EVs) present a more effective means for addressing this issue compared to load shedding. However, EVs have several limitations such as commute randomness. To ensure frequency stability and simultaneously reduce load shedding, a bi-level confidence-interval-based optimal strategy is proposed to enable the participation of EVs in UFLS, where the uncertainties of wind power and the commute randomness of EVs are estimated using a non-parametric kernel density estimation (KDE) method. In bi-level optimization, the upper level reduces the dependency on commute randomness and the wind power uncertainty during load-shedding events. Further, the upper-level solutions are sent to EV charging stations for emergency dispatch. By contrast, at the lower level, an approximation-function-based priority is proposed to optimize the task allocation. Simulation results show the advantages of the proposed approach in maintaining a stable frequency compared with traditional and adaptive UFLS schemes.

Investigation of the statistical fluctuations of the electric quadrupole transition rates of spherical nuclei by kernel density estimation method‎

In this study, the statistical correlation of the electric quadrupole transition probabilities in the spherical nuclei is investigated. To this aim, the spherical even-even nuclei in the 100 < A < 126 mass region are selected and the electric quadrupole transition rates of different levels in the ground band are determined by the interacting boson model in the U(5) dynamical limit. A non-parametric kernel density estimation method is used in the framework of nearest neighbor spacing distribution of random matrix theory to consider the statistical correlation of these quadrupole transition rates. Also, the Kullback-Leibler divergence is used to describe the regular or chaotic behavior of the considered sequences. The results show the correlation of the electric quadrupole transition probabilities between different levels of the ground band. Also, the correlation increased for such transitions that the angular momentum of the initial state of quadrupole transitions increased.

New classification method of coal spontaneous combustion three zones in the goaf based on non-parametric kernel density estimation.

The accurate division of three zones of coal spontaneous combustion in the goaf plays a vital role for coal fire prevention. Based on the O2 and CO volume fraction acquired from in situ test, this paper first fits the linear equation (characteristic equation) of O2 volume fraction with the length of the goaf. Then a cloud map of the kernel density distribution of O2 and CO volume fraction and the length of the goaf was drawn. According to the cloud map of CO, the distribution interval of CO volume fraction can be obtained, in which 0-100 ppm is the acceptable range, and greater than 100 ppm is the dangerous range, which can be used as a critical indicator for early warning of coal spontaneous combustion. According to the kernel density distribution cloud map of O2 volume fraction, there are 3 peaks of the kernel density of O2 volume fraction. According to the difference test, the 3 goaf lengths (characteristic lengths) corresponding to the 3 kernel density peaks are determined to be 12 m, 34 m, and 59 m, respectively. The characteristic O2 volume fractions are obtained by substituting characteristic lengths into the characteristic equation, which are 17.9%, 13.6%, and 8.9%. Different from the traditional dividing method, the characteristic O2 volume fractions and characteristic lengths divide the goaf into four areas: the heat dissipation zone, the first oxidation zone, the second oxidation zone, and the asphyxiation zone. The results of this study could refine the division of coal spontaneous combustion dangerous areas, reflect the dynamic change process of coal spontaneous combustion dangerous areas, and improve the efficiency of coal spontaneous combustion prevention.

Spatio-temporal dynamic evolution of carbon emission intensity and the effectiveness of carbon emission reduction at county level based on nighttime light data

Accelerating carbon emission reduction is conducive to protecting the ecological security of the Qinghai-Tibet Plateau. Based on a case study of 41 counties in Qinghai Province, China, this study explored the characteristics regarding the spatio-temporal dynamic evolution of carbon emission intensity (CEI) by using the nonparametric kernel density estimation, spatial Markov chain , and spatial variogram model and used the corrective coefficient to examine the effectiveness of the decrease of CEI. The main conclusions are as follows: First, the CEI of most counties showed a decreasing trend, although a few counties exhibited unstable CEI increase through the study period. Second, county-level changes in CEI exhibited club convergence and spatial correlation , and the county-level spatial differences in CEI narrowed. Finally, the decrease of CEI in some counties was lower than the provincial average suggesting that, even at the provincial level, the principle of common but differentiated responsibility should be observed when promoting carbon emission reduction. This study provides several recommendations to promote the sustainable development of Qinghai Province.

Real-time remaining useful life prediction based on adaptive kernel window width density

Remaining useful life (RUL) prediction plays an important role in improving the availability and productivity of systems. To improve the accuracy of real-time RUL prediction during system operation, we propose a modeling method for real-time RUL prediction based on adaptive kernel window width density. First, a non-parametric kernel density estimation (KDE) real-time RUL prediction model is proposed, and a window width model with adaptive kernel window width density is established by introducing a local density factor in the window width selection. The local density of sample points is calculated by the k-nearest neighbor distance, and the KDE is performed by adaptively selecting the window width value according to the local density of sample points in the region of non-uniform distribution of sample points. As the monitoring data changes in real time, the kernel density estimates of known samples are used to recursively update the kernel density estimates of new samples. Moreover, the logarithmic transformation of random variables and space mapping are used in the establishment of the RUL prediction model. A model of logarithmic kernel diffeomorphism transformation is established to solve the boundary shift problem of kernel estimation in the prediction to improve the prediction accuracy. Finally, the validity of the method is verified through case studies, and the accuracy of the model is judged using evaluation quasi-measures.

A novel hybrid wind speed interval prediction model based on mode decomposition and gated recursive neural network.

Wind energy has become one of the most efficient renewable energy sources. However, the wind has the characteristics of intermittence and uncontrollability, so it is challenging to predict wind speed accurately. Considering the shortcomings of traditional wind power point predictions, a new hybrid model comprised three main modules used for data preprocessing, deterministic point prediction, and interval prediction is proposed to predict the wind speed interval. The first module, the data preprocessing module, uses variational mode decomposition (VMD), sample entropy (SE), and singular spectrum analysis (SSA) to extract the different frequency components of the initial wind speed series. The second module, the deterministic point prediction module, uses extreme learning machines (ELM), and a gated recursive unit (GRU) model to perform point prediction on the wind speed series. The third module, the interval prediction module, uses the nonparametric kernel density estimation method to construct the upper and lower bounds of the wind speed interval. In addition, the final wind speed prediction interval is obtained by integrating the prediction results of multiple interval prediction results to improve the robustness and generalization of the wind speed interval prediction. Finally, the effectiveness of the prediction performance of the proposed hybrid model is verified based on the data of two actual wind farms. The experimental results show that the proposed hybrid model can obtain the appropriate wind speed interval with high confidence and quality with different confidence levels of 95%, 90%, and 85%.

Creating a Healthy Environment for Children: GIS Tools for Improving the Quality of the Social Welfare Management System.

Childhood is considered to be the most vital period for mental, physical, and social development. Even short-term deprivation of nutrition, health care, education, and affection in childhood can have long-term and irreversible negative consequences. Various social assistance programs are being launched around the world to eliminate or alleviate social problems, including those experienced by children in their immediate environment. Different solutions have been proposed around the world, but welfare systems in all countries share the following common features: social assistance is necessary and underfinanced, and social workers struggle to cope with caseloads. As a result, welfare work is stressful and not highly effective. In this study, modern Geographic Information System (GIS) tools for supporting the employees of social assistance centers (SACs) have been proposed. The data relating to welfare beneficiaries were analyzed by nonparametric kernel density estimation and divided into five datasets. The kernel density tool in ArcGIS Pro software (Esri Polska sp. z o.o., Warsaw, Poland) was used to visualize areas with a relatively high prevalence of social problems, as well as areas where the neighborhood can deliver synergistic effects. A multicriteria analysis (MCA) procedure for mapping social problems was proposed, and an algorithm was developed in the GIS environment. The generated maps deliver helpful information for supporting SAC employees, as well as monitoring, planning, and initiating preventive measures. Above all, the presented method was designed to improve living conditions by facilitating the management of welfare workers’ duties. Therefore, the proposed approach had to be effective and easy to use without an advanced knowledge of GIS tools.

Self-Attention-Based Short-Term Load Forecasting Considering Demand-Side Management

Accurate and rapid forecasting of short-term loads facilitates demand-side management by electricity retailers. The complexity of customer demand makes traditional forecasting methods incapable of meeting the accuracy requirements, so a self-attention based short-term load forecasting (STLF) considering demand-side management is proposed. In the data preprocessing stage, non-parametric kernel density estimation is used to construct customer electricity consumption feature curves, and then historical load data are used to delineate the feasible domain range for outlier detection. In the feature selection stage, the feature data are selected using variational modal decomposition and a maximum information coefficient to enhance the model prediction accuracy. In the model prediction stage, the decomposed intrinsic mode function components are independently predicted and reconstructed using an Informer based on improved self-attention. Additionally, the novel AdaBlief optimizer is used to optimize the model parameters. Cross-sectional and longitudinal experiments are conducted on a regional-level load dataset set in Spain. The experimental results prove that the proposed method is superior to other methods in STLF.

Wind Power Interval Prediction with Adaptive Rolling Error Correction Based on PSR-BLS-QR

Effective prediction of wind power output intervals can capture the trend of uncertain wind output power in the form of probability, which not only can avoid the impact of randomness and volatility on grid security, but also can provide supportable information for grid dispatching and grid planning. To address the problem of the low accuracy of traditional wind power interval prediction, a new interval prediction method of wind power is proposed based on PSR-BLS-QR with adaptive rolling error correction. First, one-dimensional wind power data are mapped to high-dimensional space by phase space reconstruction (PSR) to achieve data reconstruction and the input and output of the broad learning system (BLS) model are constructed. Second, the training set and the test set are divided according to the input and output data. The BLS model is trained by the training set and the initial power interval of training data is constructed by quantile regression (QR). Then, the error distribution of nonparametric kernel density estimation is constructed at different power interval segments of the interval upper and lower boundaries, respectively, and the corresponding error-corrected power is found. Next, the optimal correction index is used as the objective function to determine the optimal error correction power for different power interval segments of the interval upper and lower boundaries. Finally, a test set is used for testing the performance of the proposed method. Three wind power datasets from different regions are used to prove that the proposed method can improve the average prediction accuracy by about 6–14% with the narrower interval width compared with the traditional interval prediction methods.

Unbiased cross-validation kernel density estimation for wind and PV probabilistic modelling

Uncertainties associated with power generation from wind energy systems and Photovoltaic (PV) power systems present a major challenge for power system planners and operators. To account for such uncertainties, probabilistic models and probability density estimations for wind speed and solar irradiance, and their corresponding wind and PV power are highly required for long-term (multi-year) power system planning, expansion, and dispatching tools. In this article, a novel Kernel Density Estimator (KDE) model using unbiased cross-validation method for bandwidth selection is proposed for the estimation of both wind speed and solar irradiance probability densities. The estimation performance of the proposed model is assessed against the traditional parametric models (Weibull and Rayleigh distributions for wind speed, and Beta distribution for solar irradiance), and the traditional nonparametric KDE approach employing a rule-of-thumb method for bandwidth selection. The performance accuracy of all models is tested using the coefficient of determination R2, two error metrics (Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE)), in addition to the Kolmogorov–Smirnov (K–S) test that was used to assess the goodness-of-fit. The proposed approach achieved the highest percentage improvements for R2 (24% and 23%), and the lowest MAE (66% and 36%) and RMSE (63% and 25%) metrics over the popular parametric distributions for wind speed and solar irradiance, respectively, in addition to the K–S test p-values indicating a clear evidence of a good fit. Results confirm the accuracy and robustness of the probability density estimates for wind speed and solar irradiance produced by the proposed model.